Two bodies, each of mass $M$ , are kept fixed with a separation $2 L$ . A particle of mass $m$ is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is $G .$ The correct statement(s) is (are)

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The energy of the mass m remains constant

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $2 \sqrt{\frac{G M}{L}}$

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $4 \sqrt{\frac{G M}{L}}$

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $\sqrt{\frac{2 G M}{L}}$

answer is B.

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Detailed Solution

$\frac{1}{2} m V^{2} = 2 [\frac{G M m}{L}] \Rightarrow ν = 2 \sqrt{\frac{G M}{L}}$

The potential energy is a combined property of the three mass system. The kinetic energy of mass $m$ is only its energy which decreases as it moves.

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